@article{RCP25_1995__47__1_0, author = {Golse, Fran\c{c}ois}, title = {Incompressible {Hydrodynamic} {Limits} of the {Boltzmann} {Equation} : a {Survey} of {Mathematical} {Results}}, journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25}, note = {talk:1}, pages = {1--31}, publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur}, volume = {47}, year = {1995}, language = {en}, url = {http://www.numdam.org/item/RCP25_1995__47__1_0/} }
TY - JOUR AU - Golse, François TI - Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results JO - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 N1 - talk:1 PY - 1995 SP - 1 EP - 31 VL - 47 PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur UR - http://www.numdam.org/item/RCP25_1995__47__1_0/ LA - en ID - RCP25_1995__47__1_0 ER -
%0 Journal Article %A Golse, François %T Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results %J Les rencontres physiciens-mathématiciens de Strasbourg -RCP25 %Z talk:1 %D 1995 %P 1-31 %V 47 %I Institut de Recherche Mathématique Avancée - Université Louis Pasteur %U http://www.numdam.org/item/RCP25_1995__47__1_0/ %G en %F RCP25_1995__47__1_0
Golse, François. Incompressible Hydrodynamic Limits of the Boltzmann Equation : a Survey of Mathematical Results. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de M. Audin, D. Bernard, A. Bilal, B. Enriquez, E. Frenkel, F. Golse, M. Katz, R. Lawrence, O. Mathieu, P. Von Moerbeke, V. Ovsienko, N. Reshetikhin, S. Theisen, Tome 47 (1995), Exposé no. 1, 31 p. http://www.numdam.org/item/RCP25_1995__47__1_0/
[1] Mathematical Methods of Classical Mechanics ; Springer Verlag, New York (1978). | MR | Zbl
;[2] Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles; C. R. Acad. Sci. 309, 727-732, (1989). | MR | Zbl
, , ;[3] Fluid Dynamic Limits of Kinetic Equations I : Formal Derivations; J. of Stat. Phys. 63, 323-344, (1991). | MR | Zbl
, , ;[4] Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation; Comm. on Pure and Appl. Math. 46, 667-753, (1993). | MR | Zbl
, , ;[5] Fluid Dynamic Limits of Discrete Velocity Kinetic Equations; in "Advances in Kinetic Theory and Continuum Mechanics", R. Gatignol and Subbaramayer ed., pp. 57-72, Proceedings Springer Verlag Berlin (1991). | MR
, , ;[6] The Nonaccretive Radiative Transfer Equations: Global Existence Results and Rosseland Approximation; J. of Funct. Anal. 77, 434-460, (1988). | MR | Zbl
, , , ;[7] The Classical Incompressible Navier-Stokes Limit of the Boltzmann Equation; Math. Models and Methods in the Appl. Sciences 1, 235-257, (1991). | MR | Zbl
, ;[8] Density Variations in Weakly Compressible Flows; submitted to Phys. of Fluids, (1990). | Zbl
, , ;[9] The Fluid Dynamic Limit of the Boltzmann Equation; Comm. on Pure and Appl. Math. 33, 651-666, (1980). | MR | Zbl
;[10] Ph.D. Thesis, University of Arizona, (1991).
;[11] The Boltzmann Equation and its Applications; Springer Verlag, New York (1988). | MR | Zbl
;[12] Navier-Stokes Equations; Chicago Lectures in Mathematics, The University of Chicago Press, Chicago (1988). | MR | Zbl
, ;[13] Incompressible Navier-Stokes and Euler Limits of the Boltzmann Equation; Comm. on Pure and Appl. Math. 42, 1189-1214, (1990). | MR | Zbl
, , ;[14] On the Cauchy Problem for the Boltzmann Equation: Global Existence and Weak Stability Results; Annals of Math. 130, 321-366, (1990). | MR | Zbl
, ;[15] Linear Operators, Part I: General Theory; Interscience Publishers, New York (1958). | MR | Zbl
, ;[16] Solutions globales du problème de Cauchy pour l'équation de Boltzmann (d'après R. J. DiPerna et P.-L. Lions); Séminaire Bourbaki 1987-88, Exp. 699; Astérisque 161-162, 257-281, (1988). | EuDML | Numdam | Zbl
;[17] Regularity of the Moments of the Solution of a Transport Equation; J. of Funct. Anal. 76, 110-125, (1988). | MR | Zbl
, , , ;[18] Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale de l'opérateur de transport; CR. Acad. Sci. 301, 341-344, (1985). | MR | Zbl
, , ;[19] Limite fluide de l'équation de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac; submitted to Asymptotic Anal., (1991). | MR | Zbl
, ;[20] On the Fluid Dynamic Approximation to the Boltzmann Equation at the Level of the Navier-Stokes Equation; Commun. in Math. Phys. 70, 97-124, (1979). | MR | Zbl
, , ;[21] Comm. on Pure and Appl. Math. 34 p. 481, (1981); | MR | Zbl
, ;Comm. on Pure and Appl. Math. 35 p. 629, (1982) | MR | Zbl
, and[22] Sur le mouvement d'un fluide visqueux emplissant l'espace ; Acta Math. 63, 193-248, (1934). | JFM | MR
;[23] Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod (Paris 1965). | Zbl
;[24] Fluid Dynamic Limit of the Nonlinear Boltzmann Equation at the Level of the Compressible Euler Equation; Commun, in Math. Phys. 61, 119-168, (1978). | MR | Zbl
;[25] Global Existence to the BGK Model of the Boltzmann Equation; J. Diff. Eq. 82, 191-205, (1989). | MR | Zbl
;[26] Résultat d'existence pour le modèle de BGK de la théorie cinétique des gaz en domaine borné et non borné; preprint, (1991).
;[27] Formation of Singularities in 3D Compressible Fluids; Commun. in Math. Phys. 101, 475-485, (1985). | MR | Zbl
;[28]
: Conference at the IVth Workshop on Mathematical Aspects of Fluid and Plasma Dynamics; Kyoto (1991).[29] Asymptotic Theory of Flow of Rarefied Gas over a Smooth Boundary II; in "Rarefied Gas Dynamics", D. Dini ed., 737-749, Editrice Tecnico Scientifica, Pisa (1971).
:[30] Steady Gas Flows past Bodies at Small Knudsen Numbers; Transport Theory and Stat. Phys. 16, 189-199, (1987). | Zbl
, :[31] A Remark Concerning the Chapman-Enskog Asymptotics; in L. Desvillettes, Thèse d'habilitation, preprint Ecole Normale Supérieure, D.M.I., (1994). | MR | Zbl
, :